… In the sequel, we shall recall certain useful results, such as the relations among transition
probabilities in the presence and in the absence of catastrophes. More specifically, in
Section 2 we shall introduce a birth–death process with catastrophes { N ( t ) ; t ≥ 0 } with
state space S = { 0 , 1 , 2 , … } , and shall outline various functional relations that allow us to
describe N ( t ) in terms of the birth–death process { N ̂ ( t ) ; t ≥ 0 } defined on the same
state-space S and characterized by the same birth and death rates as N ( t ) , but for which …